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Figures
- Fig. 1.
Experimental set-up to determine compensatory head roll movements in Polistes wasps. (A) Wasps were tethered by waxing a strip of cardboard to their thorax and mounted onto the shaft of a servo motor, which was used to rotate the body of the wasp. Wasps viewed different visual scenes (B): a natural, outdoor environment (B1), a cluttered and artificially lit indoor laboratory environment (B2), a regular pattern of black and white stripes inside an opaque tube (B3), an artificial horizon (B4), a homogeneous white background (B5), or a completely dark environment (B6). Patterns inside an opaque horizontal cylindrical drum were illuminated with a fibre-optic ring-light and three pairs of infrared LEDs (in case of B6). Wasps were filmed head-on with a digital movie camera at 50 or 120 frames s−1. (C) Sample images of head and body orientation in the two visual conditions outdoors and with a uniform white pattern. The points on the head and the holding structure that were used to determine orientation are marked by red dots. Note the lack of head roll compensation in the uniform condition. (D) The velocity profile of the chirp signal applied to the servo motor (see Materials and methods for details). (E) Three snapshots from movie records of male Polistes in free flight. The head and the tip of the abdomen are marked by red and yellow dots, respectively. Their horizontal distance (x), together with independent measurements of the length of the wasps' body long axis (l) was used to estimate the yaw axis orientation (ϕ) of wasps (see schematic on the right). The points used to determine head orientation and body roll orientation are marked with blue dots.
- Fig. 2.
Time course of head roll responses to sinusoidal, frequency modulated (chirp) oscillations applied to the body. In each of the four visual conditions indicated by pictograms (see Fig. 1B for explanation), the mean and s.d. (coloured envelope) of body orientation (blue), of head orientation (red) and of head orientation relative to the body (black and green) were plotted. The chirp signal frequency increased from 0.2 to 2 Hz in 20 s. Number of wasps and number of chirp runs averaged are given for each panel.
- Fig. 3.
Dynamic properties of the head roll response. (A) The mean chirp responses of the head in the four visual conditions: outdoors, room light, black/white stripes and horizon. (B) Bode diagram for the gain computed from the time course of responses shown in A. Thick lines are means and coloured areas are means ± s.d. Dotted line indicates perfect compensation of the head at 0 dB. (C) Bode diagram for the phase (perfect compensation at −180 deg indicated by dotted line); otherwise conventions as in B. Bode diagrams for the gain (D) and phase (E) for three stimulus repetitions outdoors obtained for one wasp.
- Fig. 4.
Head roll responses in a uniform bright environment and in the dark. (A) Time course of head roll responses to sinusoidal, frequency-modulated (chirp) oscillations applied to the body. Conventions as in Fig. 2. (B) Autocorrelation of body oscillations (blue) and cross-correlation of body oscillation against the negative values of head movements relative to the body (red dotted line), for the ideal case: θbody(t) = −θheadbody(t). The quality of compensation is indicated by a high correlation coefficient with some delay. Number of wasps and number of responses as in Fig. 2 for conditions horizon, stripes, indoor and outdoor. Uniform: responses obtained from three wasps (N=3) and three chirps in total (n=3). Dark: responses obtained from two wasps (N=2) and two chirps in total (n=2).
- Fig. 5.
Head roll responses of three wasps (top to bottom row) to step body rotations outdoors (left column), in a cylinder with black and white stripes (centre column) and in the dark (right column). Blue: body orientation; black: head orientation; red: head orientation relative to body.
- Fig. 6.
Modelling head roll stabilization. (A) Left: block diagram of the head stabilization system in Polistes wasps based on two nested visual feedback loops. Right: transfer functions of the block diagram described on the left for model responses shown in B with s as the Laplace variable. The inner feedback loop receives input on head angular speed (Ωheadout) measured by motion-sensitive neurons [HMS(s)] while the input to the outer feedback loop is the head orientation (θheadout) that could be measured by the tonic dorsal light response mediated by the compound eyes. The visual regulator Cv(s) is a simple first-order low-pass filter removing the high-frequency components amplified by the derivative action of HMS(s). The head dynamics are modelled by a first-order low-pass filter with a time constant of 5 ms compatible with the low inertia and mass of the head. (B) Model performance compared with wasp step responses in outdoor and in black and white stripe conditions. Model responses θhead(t) (thick grey lines) and θheadbody(t) (thick red lines) were computed by taking measured body orientation θbody(t) (blue lines) as input disturbance for the two nested visual feedback loops. Otherwise conventions as in Fig. 5.
- Fig. 7.
Head roll control in free flight. (A) Time course of body orientation relative to vertical (blue), head orientation relative to horizontal (red), the inverse of head orientation relative to the body (black) and the yaw orientation of the body longitudinal axis (green) of patrolling Polistes males for four example sequences recorded at 300 frames s−1. The sequence in the top panel has been digitized five times, with means (thick lines) and s.d. (shaded areas) shown in equivalent colours. Inset numbers are mean s.d. for the four variables. The horizontal grey areas in all panels mark ±10 deg. (B) Left: histograms of head orientation relative to horizontal (red) and body orientation relative to vertical (blue); right: histograms of angular velocity of head (red) and body (blue); data from 13 sequences, where wasp yaw orientation was within ±10 deg parallel to the optical axis of the camera; 3.75 s total flight time. (C) Mean cross-correlation functions (black dotted lines) with s.d. (grey shaded areas) for the same data set as used in (B). Left: head orientation relative to the body (θheadbody) against body orientation (θbody); right: head angular velocity relative to the body (θheadbody/dt) against body angular velocity (θhead/dt). (D) Expanded block diagram of the proposed head stabilization system in Polistes wasps including a feed-forward controller Cf(s) that leads in principle to an exact compensation of head orientation (θheadbody) during spontaneous rotations of the body (θbody). The common drive signal Uroll controls both head and body roll orientation, while the two nested visual feedback loops (see Fig. 6A) provide an absolute orientation reference and correct any remaining slip speed (for details see text). Without any recording of the signal Uroll, model responses θhead(t) (thick grey lines) and θheadbody(t) (thick red lines) plotted in A were computed by taking measured body orientation θbody(t) (blue lines) as input signal for Cf(s) and as input disturbance for the two nested visual feedback loops.
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